Algorithmic aspects of branched coverings

DOI10.5802/afst.1566zbMath1422.57004arXiv1512.05948OpenAlexW2963892711MaRDI QIDQ4609689

Dzmitry Dudko, Laurent Bartholdi

Publication date: 23 March 2018

Published in: Annales de la Faculté des sciences de Toulouse : Mathématiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.05948

zbMATH Keywords

surveybranched coveringsbisetsThurston maps

Mathematics Subject Classification ID

Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Low-dimensional topology of special (e.g., branched) coverings (57M12) Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes (57-02)

Related Items (12)

Algorithmic aspects of branched coverings. II/V: Sphere bisets and decidability of Thurston equivalence ⋮ Invariant spanning trees for quadratic rational maps ⋮ Invariant graphs of rational maps ⋮ Algorithmic aspects of branched coverings IV/V. Expanding maps ⋮ Origami, affine maps, and complex dynamics ⋮ Algorithmic aspects of branched coverings ⋮ Centralizers in mapping class groups and decidability of Thurston equivalence ⋮ Modular groups, Hurwitz classes and dynamic portraits of NET maps ⋮ Rationality is decidable for nearly Euclidean Thurston maps ⋮ Expansion properties for finite subdivision rules II ⋮ Algorithmic aspects of branched coverings. III/V: Erasing maps, orbispaces, and the Birman exact sequence ⋮ Recognizing topological polynomials by lifting trees

Uses Software

• GAP
• IMG

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• From rubber bands to rational maps: a research report
• Thurston's pullback map on the augmented Teichmüller space and applications
• Thurston equivalence of topological polynomials
• Iterated monodromy groups of quadratic polynomials. I.
• Surfaces and planar discontinuous groups. Revised and expanded transl. from the German by J. Stillwell
• On the classification of homeomorphisms of 2-manifolds and the classification of 3-manifolds
• A proof of Thurston's topological characterization of rational functions
• Train-tracks for surface homeomorphisms
• Combinations of complex dynamical systems
• Algorithmic aspects of branched coverings I/V. Van Kampen's theorem for bisets
• An algebraic characterization of expanding Thurston maps
• Tan Lei and Shishikura's example of non-mateable degree 3 polynomials without a Lévy cycle
• Questions about polynomial matings
• Topological characterization of canonical Thurston obstructions
• Nearly Euclidean Thurston maps
• Homotopy shadowing
• Critical portraits for postcritically finite polynomials
• On the geometry and dynamics of diffeomorphisms of surfaces
• Matings of quadratic polynomials
• A Family of Cubic Rational Maps and Matings of Cubic Polynomials
• Algorithmic aspects of branched coverings
• Algorithmic Construction of Hurwitz Maps
• Thurston equivalence to a rational map is decidable
• The Thurston equivalence for postcritically finite branched coverings
• Constructive geometrization of Thurston maps and decidability of Thurston equivalence

This page was built for publication: Algorithmic aspects of branched coverings